Identifying stable coexistence in empirical systems is notoriously difficult. Here, we show how spatiotemporal structure and complex system dynamics can confound two commonly used stability metrics in empirical contexts: response to perturbation and invasion rate when rare. We use these metrics to characterize stable coexistence across a range of spatial and temporal scales for five simulated models in which the ability of species to coexist in the long term is known a priori and for an empirical old field successional time series. We term the resulting multivariate distribution of metrics a "stability fingerprint." In accordance with a wide range of classic and recent studies, our results demonstrate that no combination of empirically tractable metrics or measurements is guaranteed to "correctly" characterize coexistence. However, we also find that heuristic information from the stability fingerprint can be used to broadly characterize dynamic behavior and identify circumstances under which particular combinations of species are likely to persist. Moreover, stability fingerprints appear to be particularly well suited for matching potential theoretical models to observed dynamics. These findings suggest that it may be prudent to shift the focus of empirical stability analysis away from quantifying single measures of stability and toward more heuristic, multivariate characterizations of community dynamics.